I got my private registration plates fitted today then went onto the DVLA site and transferred it with them. It is so much easier to do things online with the DVLA. Unfortunately, I will have to wait until tomorrow to inform my insurance but as I am unlikely to be using the car until Thursday, that's not a problem.
What was a problem was getting the old number plates off. Both the RH screws had badly rusted heads and I was unable to see if they were security screws. I removed the front with a pair of pliers but the rear was solid and once I got it turning was turning the plastic insert in the body. I had to resort to the centuries-old, tried and tested method. A hammer and chisel!